Let's solve each equation step by step:

1) 4x - 7 = 2x + 15

Subtract 2x from both sides to isolate x:

2x - 7 = 15

Add 7 to both sides:

2x = 22

Divide by 2:

x = 11

2) 7x + 12 = 10x - 3

Subtract 7x from both sides to isolate x:

12 = 3x - 3

Add 3 to both sides:

15 = 3x

Divide by 3:

x = 5

3) 11 - x = 55 + x

Add x to both sides:

11 = 55 + 2x

Subtract 55 from both sides:

-44 = 2x

Divide by 2:

x = -22

4) -35 - 2x = 42 + 9x

Add 2x to both sides:

-35 = 42 + 11x

Subtract 42 from both sides:

-77 = 11x

Divide by 11:

x = -7

Therefore, the solutions to the equations are:
1) x = 11
2) x = 5
3) x = -22
4) x = -7